Orsogato makes good points-- you can buy a useful home defense rig
and a very utilitarian deer rig for the price of many other single-gun choices.
But that doesn't really follow the parameter you set, and we're supposed to play be the rules... so:
While an Armalite AR-10 in .308 with a .243 upper would be a nice answer to your quandry as far as single-gun utility goes, it might not be legal in your state to hunt with an auto, and is prohibitively expensive. Also, it has the disadvantage (for some) of being "evil looking," and possibly bannable in some areas. So nix that.
Frankly, I like Paul's approach-- get yourself a full-sized thutty-thutty, and get good with it. You can gussy it up with a trigger job, good sights, a sling, a side-carrier, maybe even scope mounts and a low-powered scope for deer season. If you really want more shots, perhaps the .44 or .45 is the way to go-- both will kill deer cleanly within 100 yds.
If you get one with one of those damnable safeties, super-glue the thing open, load the magazine, and leave the chamber empty.
Other than that, my SKS is my brother-in-law loaner-deer rifle, and would work well. But that's a cheapskate's way out...
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Will you, too, be one who stands in the gap?
Matt